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The Chirikov criterion or Chirikov resonance-overlap criterion was established by the Russian physicist Boris Chirikov.Back in 1959, he published a seminal article, [1] where he introduced the very first physical criterion for the onset of chaotic motion in deterministic Hamiltonian systems.
Chaos theory has been used for many years in cryptography. In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. These algorithms include image encryption algorithms, hash functions, secure pseudo-random number generators, stream ciphers, watermarking, and steganography. [123]
Notice the appearance of a "dotted" zone, a signature of chaotic behavior. Orbits of the standard map for K = 0.6. Orbits of the standard map for K = 0.971635. Orbits of the standard map for K = 1.2. Orbits of the standard map for K = 2.0. The large green region is the main chaotic region of the map. A single orbit of the standard map for K=2.0.
Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal.
The Duffing equation is an example of a dynamical system that exhibits chaotic behavior. Moreover, the Duffing system presents in the frequency response the jump resonance phenomenon that is a sort of frequency hysteresis behaviour.
Computed regular (non-chaotic) Rydberg atom energy level spectra of hydrogen in an electric field near n=15. Note that energy levels can cross due to underlying symmetries of dynamical motion. [4] Computed chaotic Rydberg atom energy level spectra of lithium in an electric field near n=15. Note that energy levels cannot cross due to the ionic ...
Boris Chirikov was born in the city Oryol, Russia, USSR.Graduated from the Moscow Institute of Physics and Technology in 1952, he worked with Budker at the Kurchatov Institute and moved with him to Siberia in September 1959 to work at the Institute founded by Budker in Akademgorodok, Novosibirsk (now Budker Institute of Nuclear Physics).
Bunimovich introduced absolutely focusing mirrors, which is a new notion in geometric optics, and proved that only such mirrors could be focusing parts of chaotic billiards. [5] He also constructed so called Bunimovich mushrooms, which are visual examples of billiards with mixed regular and chaotic dynamics.